1. Activity Set 2.4 PREP PPTX Visual Algebra for Teachers

2. Chapter 2 LINEAR EXPRESSIONS, EQUATIONS AND GRAPHS Visual Algebra for Teachers

3. Activity Set 2.4 Linear Expressions and Equations Visual Algebra for Teachers

4. PURPOSE To learn how to:  Work with, and model, sequences of black and red tile figure  Find representations of general figure  Answer algebraic questions about the tile sequences and  Graph input/output pairs.  To learn to use function notation to express input and output relationships.

5. Black and red tiles and black and red n-strips MATERIALS

6. INTRODUCTION

7. Functions / Function Notation A function is a rule that for each input gives a unique output. The tile sequences we have been looking at can be thought of as having an input (figure number) and output (net value of the figure). Since the total number of tiles, and the corresponding net value, in a given figure does not change, for each input, there is a unique output. We can think about our tile figure sequences as visual representatives of a function relationship.

8. Functions / Function Notation The function input and output relationship is usually denoted symbolically in a form such as: In this example; f stands for function n is the input or independent variable and T is the output or dependent variable.

9. Functions / Function Notation The name of the function is not fixed. Functions are not all named f. Functions can be named using any letter, names such as Chairs, Tees and Rectangles or letters such as C, T and R intended to denote names or other identifying features. The symbolic presentation of a function relationship is a convenient shorthand notation that allows us to write in a few symbols the meaning of an entire sentence.

10. Using Function Notation The function notation (shorthand) for denoting (for example) “the 5th Chair figure has a net value of 9” is C(5) = 9. Note that in this example, “Chair” was named by the function name C.

11. Modeling with Red n-Strips A sequence of tile figures whose nth figure is modeled by a red n-strip might look like one of the following horizontal or vertical sets of tile figures:

12. Modeling with Red n-Strips

13. Modeling the nth Figure Using Red n-Strips to Model the nth Figure of a Tile Sequence The red n-strip can be all or part of the nth figure for a tile sequence and can be combined with other algebra pieces and black and red tiles. An nth figure might look like this:

14. Modeling with B & R n-Strips A sequence of tile figures such as the following combines the use of black and red tiles; Hence, in the next example, this nth figure combines the use of black n-strips and red n-strips. In this sequence of tile figures we are looking at the pattern and we are not concerned about reducing the figures to minimal collections of black or red tiles.

15. Modeling with B & R n-Strips

16. Sketching Black/Red n-Strips To sketch black and red n-strips, you may wish to simply sketch an outline of the strip. Label a black n-strip with a B for black. Label a red n-strip with a R for red

17. You are now ready for: CLASS NO PREP QUIZ 2.4 Visual Algebra for Teachers